A method to calibrate analytical models of multi-story buildings from earthquake records

Abstract

For multi-story buildings, the standard approach to develop analytical models from earthquake records is to match the modal characteristics (i.e., modal frequencies, damping ratios and mode shapes) of the model with those identified from the data. Typically, the response of the building is recorded in the basement, roof and a few intermediate floors. When the number of the instrumented floors is less than the total number of floors, an analytical model cannot be constructed uniquely. In other words, more than one model can match the recorded response. This study presents a new method based on the transfer matrix formulation of the response. The method requires that vibration time histories are known at every floor. Since they are typically not recorded at every floor, we first present a methodology to estimate vibration time histories at non-instrumented floors from those of the instrumented floors. We assume that, at each modal frequency, the mode shape of a multi-story building can be approximated as a linear combination of the corresponding mode shapes of a shear beam and a bending beam. We determine the combination factors by using the least-squares approximation to the mode shapes identified from the records. The accuracy of the methodology is tested by using recorded motions from two buildings that have instruments at every floor. Assuming that only a few floors had instruments, the vibration time histories at other floors are calculated and compared with the recorded time histories. The results of the methodology are also compared with those from other approximation techniques, such as linear or cubic interpolations, and found to be much superior. Once the vibration time histories are known at every floor, we present a new approach to calibrate analytical models of multi-story buildings based on the transfer matrix formulation of the response. The methodology utilizes top-to-bottom spectral-ratios at each story and shows that these spectral ratios are not influenced by any structural changes in the stories below. Thus, starting from the top story, the stiffnesses of each story can be determined uniquely by matching the dominant frequencies of the spectral ratios, assuming that the mass of each floor is known or estimated. A numerical example is presented to confirm the validity of the approach. The study proves that the story stiffnesses of a multi-story building can be determined uniquely by using vibration records taken from only a few floors.